Achievable rates of MIMO downlink beamforming with non-perfect CSI: a comparison between quantized and analog feedback

We consider a MIMO fading broadcast channel and compare the achievable ergodic rates when the channel state information at the transmitter is provided by "analog" noisy feedback or by quantized (digital) feedback. The superiority of digital feedback is shown whenever the number of feedback channel uses per channel coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a minor effect even by using very simple uncoded modulation. Finally, we show that analog feedback achieves a fraction 1- 2F of the optimal multiplexing gain even in the presence of a feedback delay, when the fading belongs to the class of "Doppler processes" with normalized maximum Doppler frequency shift 0 les F les 1/2.